Speculation linking Carlos Vela with a return to Arsenal has ended after Real Sociedad confirmed that the Mexican forward has signed a new four-year contract with the club.

Having sold Vela to the Spanish club in 2012, Arsenal were widely expected to activate a £3.5m buy-back clause this summer, but Sociedad have reportedly paid £8.8m, plus a further £4m in possible performance-related bonuses, to remove the clause and ensure that the 25-year-old remains in Spain.

In a statement released on their website, the La Liga club confirmed: “Real Sociedad have reached an agreement with Arsenal FC which will allow Carlos Vela to continue at the club on a permanent basis. The player meanwhile, has signed a contract extension which ties him to Real Sociedad for the next four seasons. The player’s previous contract was due to expire in June 2016. The Mexican striker has now formally signed his new contract.”

Initially joining on loan in 2011, Vela became an integral member of Sociedad’s squad and last season contributed 21 goals and 13 assists in all competitions.

“I’ve always said that this is my home,” he told the club’s website. “I am very happy in San Sebastián, which I told the president when he asked for my intentions.

“We knew it would not be easy, but thankfully it is resolved and all parties are happy. This club, this team has the ambition to make it better, and I am convinced that we will perform an exciting year.

“Now I get to enjoy my last days of vacation with my family to come with great force and to prepare this great year in the best way.“